Question

1. graph: $x>-4$
2. graph: $x\geq -2.5$
3. graph: $5
4. graph: $\frac{1}{4}\geq x$
5. graph: $x<-1$

Explanation:

Step1: Graph \(x > - 4\)

For \(x > - 4\), we use an open circle at \(x=-4\) (because \(-4\) is not included in the solution set) and draw an arrow to the right (since \(x\) is greater than \(-4\)).

Step2: Graph \(x\geq - 2.5\)

For \(x\geq - 2.5\), we use a closed circle at \(x = - 2.5\) (because \(-2.5\) is included in the solution set) and draw an arrow to the right (since \(x\) is greater than or equal to \(-2.5\)).

Step3: Graph \(5 < x\) (which is equivalent to \(x>5\))

For \(x > 5\), we use an open circle at \(x = 5\) (because \(5\) is not included in the solution set) and draw an arrow to the right (since \(x\) is greater than \(5\)).

Step4: Graph \(\frac{1}{4}\geq x\) (which is equivalent to \(x\leq\frac{1}{4}\))

For \(x\leq\frac{1}{4}\), we use a closed circle at \(x=\frac{1}{4}\) (because \(\frac{1}{4}\) is included in the solution set) and draw an arrow to the left (since \(x\) is less than or equal to \(\frac{1}{4}\)).

Step5: Graph \(x < - 1\)

For \(x < - 1\), we use an open circle at \(x=-1\) (because \(-1\) is not included in the solution set) and draw an arrow to the left (since \(x\) is less than \(-1\)).

Answer:

1. Open circle at \(-4\), arrow to the right.
2. Closed circle at \(-2.5\), arrow to the right.
3. Open circle at \(5\), arrow to the right.
4. Closed circle at \(\frac{1}{4}\), arrow to the left.
5. Open circle at \(-1\), arrow to the left.